Question

The function f(x) = x2. The graph of g(x) is f(x) translated to the left 6 units and down 5 units. What is the function rule for g(x)?
g(x) = (x - 6)2 + 5

g(x) = (x + 6)2 - 5

g(x) = (x - 5)2 + 6

g(x) = (x + 5)2 - 6

Answer 1

Please use x^2 to denote "square of x."  x2 has no meaning in algebra.

f(x) = x^2. The graph of g(x) is f(x) translated to the left 6 units and down 5 units.  If we translate the graph of f(x) = x^2 6 units to the left, we get the new function g(x) = (x+6)^2.  If, after that, we move the entire graph down 5 units, we get the new function   h(x) = (x+6)^2 - 5    (answer)